Thanks, I was commenting from the perspective that if everyone had a connection with spirit there would be no need for the division. If all was enlightened/One, then of what purpose would be the separation?

Originally Posted by Androgynus

OR, alternatively, you could resort to the unheard of measure of hitting the 'Post Reply' button ONLY one time, even if it takes a while before the screen resets with your message on it

The pyramid could be balanced by a "water pyramid" with sheep on top,
making a hexagram.

The pyramid still reveals a chain of connection and interdependence.
Can there really be a top in interdependence or is that an illusion/agreement,
merely psychological?
I see it is so.
I think sex is not adequately represented in that pyramid.

Let me provide an example of how triangles have been or might have been learned, depending on your own experience. I first learned triangles by learning their form, as they were drawn on the blackboard by the teacher and the students, or cut out of paper with scissors. There were many kinds of triangles, of different shapes and sizes, but all were composed of drawn line segments with three angles. In later grades, I learned that real triangles in mathematics were not drawn, but were “imagined” since they were made up of lines that had no width (or depth), and thus could not be seen. A drawn triangle was an image of the “real” triangle that was only “seen” in the imagination. Triangles were mental concepts. Imagination of the generalized triangle was required in order to grasp the idea of the real triangle—abstractions, of which the “triangle” itself was an idea.

We thus learned that triangles are only represented when we “draw” them, even if we first learned of triangles as if they were real since they could be drawn on paper.

Today, I continue to see the drawings as both representations as well as real triangles, and this helps me when doing geometric exercises that require the use of triangles. I understand better how in the Middle Ages, people actually saw the wine turn to blood and the bread turn to Jesus’ flesh, in Holy Communion. I can see the world with a two-fold vision: the metaphoric and the “real,” the imagined and the “actual.”

My idea of triangles changed as we progressed through school. But even then, I saw a drawn triangle as a real “triangle” as well as “merely” a representation of an abstraction that is a “real” triangle. I learned to see the representations as a “metaphor,” much like how we might see a skillful dancer in Firebird, for a moment become the Firebird, and be moved by the art involved. The triangle that I saw on the paper was for me a real triangle, and not something like a real triangle. It too enchanted me as a metaphor, and so I appreciated the Pythagoreans, who saw mathematics as mystical and as having deep mysteries that expressed human existence.

A line or point can’t really be drawn in the world of “pure” geometry, and if you can’t see a line or a point, then it follows that an “angle” is also imaginary since it can’t be touched or seen. If you think about this process, it seems uncanny: we like to think of the world as composed of things—of things that can be directly perceived. The “outline” and the “angle” are the result of acts of imagination.

We need then to recognize that when children first learn to draw triangles, they are following an implicit or explicit command, or injunction—i.e. “draw a triangle” even if in pure mathematics, forms can’t be “drawn.” As more triangles are drawn, the concept of “triangle” is soon understood, sometimes so quickly that we forget it involves imagination. Imagination is an act of our minds, whereby we recognize patterns, even if the “matter” that makes the pattern visible is not material. Calligraphy in Japan is traditionally taught this way, and so writing itself involves not only repetition and rote, but also a practice in attaining some kind of aesthetic insight into brush-stroking a written character. As one becomes adept at using the brush, the entire act becomes like good choreography that expresses both the past and tradition, and also an act that is personal and expresses one’s own unique spirit. Triangles and circles are also sometimes brushstroked by Zen Buddhist artists, as well as Chinese characters or kanji.

Once triangles become part of culture, they become a given, an abstraction that can even be imagined without being constructed—seemingly losing its dependence on time and being “eternal” as it was for Plato. With globalization, triangles become universally recognized by all school children, and their “reality” is further validated through our built environment such that triangles, for example, become a part of the architecture of every day life, found in many objects invented by human beings. In some ways, we have been seduced into a Platonic universe where only ideal forms, forms that have no materiality exist; yet we deal with drawn triangles in everyday life—the abstract has become material” seducing us back into the world of material reality. It is as if the real lived contemporary world in which concepts like “triangles,” “lines,” “numbers” are found was a given, rather than ideas that evolved from imagination and experience.

A triangle is like a smile—like the Cheshire Cat’s grin in Alice in Wonderland, where the smile first appears on the face of the Cheshire Cat, sitting on a tree branch. We know what a cat is like and what sort of outline a tree branch is—we’ve experienced and learned such matters; but Lewis Carroll’s story makes parts of the cat gradually vanish, in stages, starting with its tail, until the entire cat vanishes for Alice, except for its grin, which remains and which she perceives. I smile as I write this story, and the story itself becomes a smile. If I extend my facial movements of a smile into my whole body, and move, I become a dancer and a choreographer at the same time. I create a space that is a smile.

Similarly in the world of pure plane geometry, triangles are no longer drawn, but are “merely” represented by drawn lines that have three dimensions (since the pencil line has a minute degree of depth). A drawn triangle thus has now become only a representation of a “real triangle.” Yet the drawn triangle has the status of a metaphor— it is indeed perceived as a triangle, and not merely, as in a simile, like a triangle. It is a form –actually an idea that persists now almost forever in our collective cultural memory.

In short, we have learned this abstraction so that the injunction part—so important in its evolution, is no longer required. At this point, it might be asked: perhaps we need to teach the idea of a triangle proceeding from drawing “triangles” to redefining them later as abstractions, so the imaginative evolution is historically recapitulated in a speeded up way, as in pedagogies of the past, including that developed by Rudolph Steiner in his Waldorf school.

Thus, imagination has in one sense been converted into “nature” when the abstractions come to represent “objective” reality. And this is what angered Blake, when the idea of “nature” as a scientific-mathematical “ratio” became dominant and “real” and it became the task of scientists to discover its natural rationality. The invented universe imposed upon it by human rationality became increasingly the lived world that destroyed vitality and faith.

We need to be reminded that the basis for the abstractions that become reality are rooted in the living body of the child, when the child first learns to draw such things as triangles and other “things.” Images are not the thing itself. Images are rooted in the original injunctions, the directions or commands (implicit or explicit) that make us relate to the abstractions, while at the same time furthering our entry into the pure world of the mathematical system.

But where is the point of contact with the world within the world? The meshing takes place at the edge. The mesh is the place where we tangle with the world. But we are ‘on edge’ ‘enmeshed’ in the world. What of the edge? The edge is not before the thing. The edge is not after the thing. The edge of a definite thing is an indefinite thing. But the edge of an indefinite thing is a definite thing. Definition: the edge is the essentially narrow part of the thing (as the surface is the essentially thin part of the thing). The edge separates the greater part of the thing from not-the-thing. The edge of a thing is not to be confused with what is at the edge of the thing. The bank of a stream is not the edge of the flow. The edge of the stream is precisely that essential narrowness of the stream by which it separates itself from the emptiness-of-the-flow that is the land. The edge of the land interacting with the edge of the stream is the real indefiniteness of the respective edges of definite stream and definite land, reflecting the functionally irreducible distinction of perception and conception (the latter, in turn, a function of an irreducibly ‘functional’ self), respectively, the indefinite edges of two definite things at the point of contact supported by their infinitely indefinite separation (= almost nothing between), and, conversely, the definite edges of two indefinite things at the point of contact supported by their absolute separation (= nothing between). But now for the first time ‘nothing’ is no more. Now for the first time ‘almost nothing’ is no more. Now in history the beginning of the conception of resistance identical with the zero resistance of the medium to the flow. What now actually exists is the elimination of the necessity of reducing the motion of the world to ’nothing’ or to ’almost nothing’ in order to defeat the consequences of an inertial framework. The construction of the frame of reference is the essence of motion ex nihilo, that is following nothing, not ’not made out of anything’, not made out of nothing (European consciousness), but also not made doubly redundantly of matter, not ‘not made out of almost nothing’, i.e., not ‘not created but fashioned’ (American consciousness), but the unprecedented construction of the frame of reference made out of actual existential matter: motion itself beginning to be constructed (New World consciousness). Now conceived for the first time: the reduction to ‘nothing’ or nothing ‘almost’ itself of the elimination of motion identically the perfect ordering of motion: neither the ideal definite, ‘nothing’, nor the real indefinite ‘almost nothing’, at the vanishing of the points between the edges, respectively, of two indefinite and two definite things, but the infinitely shared edge, the existence itself of order. The threshold of a new universe is traversed for the first time.

[snip]

But for the first time, just in time, the edge of mind is a consciousness the edge of which is absolute. The edge is essentially perfect as never before. For the first time in history the fact is perceived that the essentially narrow part of mind is the edge of consciousness now after nothing. Mind is absolutely edged out of the edge after nothing. As never before the edge of the ocean is the edge of an absolute stream: the explosion of the universe itself, the advent of genetic engineering, the beginnings of the practicability of superconductivity, the incipient technology of thinking: there is no land the stream passes through, no same, neither in imitation of the stream to ‘pass through’, nor to occupy in refusing to imitate the stream, neither to seize upon nor to seize: the banks are identical with the stream for the first time: in the cosmological flood of the stream of consciousness both banks flow as the stream itself flows: there is neither the possibility of an absolute hanging back from a sameness, the same ‘hanging back from’ nor the possibility of “participating in the flow” which possibility is already too much of a “hanging back,” a hanging back from the flow in the relationship to the flow, the same ‘taking part’. Now for the first time in history the Christ is the god of the stream: thought in essence for the first time, the Christ of the stream eliminates the ‘eternal death of Jesus’: not the god of this or that stream but the god of the stream of existence itself beginning the absolute elimination of the death of God. As never before the divine flows absolutely. In this flow every notion of self is dissolved. The nakedness of the species is entirely eliminated. There remains neither the ‘almost nothing’ enveloped in the pure ‘nothing’, nor the pure ‘nothing’ enveloped in ‘almost nothing’. The consciousness of man is the creating edge. The essentially narrow part of man, the narrow itself of man - the edge by which man grows is existing ex nihilo. What now actually occurs is the perfect envelopment of the beginning of the Torah which speaks essentially. The totality of being after nothing, the totality not after (either) being (or) nothing (the totality of being not after ‘either nothing or…’) i.e., not from/out of nothing is the absolutely existing edge, the edge every part of which is identical with the edge itself.

What now for the first time is conceived essentially is the Apocalyptic vision: there is no temple in the city, nothing whatsoever is hidden, the body itself is clothing itself, clothes do not cover the body but reveal the essence of the body, manifest the essentially art factual structure of the body, reveal the world to be such a novelty that man cannot stand even so much apart as to be a participant, so as to (merely) take part in the creation of the world, avoiding thereby the absolute responsibility of creating a new world. The literal truth of the fact that the body is the temple of the divine spirit now begins to be understood: since the divine spirit, qua first-time experience of the perfect edge of the other, takes up no room whatsoever, there is no end to the art factual surface of the body in the so-called ‘interior depths’. The essentially thin part of the art factual body (surface) is its essentially narrow part (edge) infinitely after nothing. The reality of the body is the absolutely unconditioned exteriority of the world. Humanity can hide no longer in its clothes, nor in its nakedness: everything begins to be fabricated. For the first time the network is absolute. The essentially narrow part of existence ex nihilo exists everywhere. The edge of consciousness begins to be an essential objectivity, not the edge of mind, but the edge sharing the edge of the other for the first time, the edge of the mind of the other, transcending the ‘functionally’ self-referential polarity of the definite/indefinite vanishing of separation at the point of contact, eliminating for the first time this vanishing of separation by sharing the edge after nothing of the essentially different reality of the other, experiencing the other as identical with the novelty of every part of the edge. For the first time the transcendental is absolutely separate from the edgeless. Thought is the edge of the thing. Consciousness, at once absolute, begins to share the edge of the mind of another consciousness. After nothing the absolutely from-less totality: for the first time the perfect elimination of the space of time: no possibility of the essential redundancy of placing time: whether inside an exterior space, “a totally present objectivity” dissociated from all…interior identity,” or “outside an interior” which has been made “out place.” Time is absolutely the place. For the first time the Ego, minus the a priory, transcendental other, is absolute act. To create the absolute edge is to begin to operate essentially without reference to self: time after nothing is neither not ‘our’ now, nor ‘our’ place. The infinitely shared edge has no within to be eternally outwardized, and a fortiori no within to transform existence into a body in the absence of the divine spirit ideally interiorizing the world. The absolute exteriority of time-consciousness is the resurrection itself of the Body of the Finite God absolutely at the disposal of another. For the first time the clearly perceived reality is that objectivity is to create objectivity itself. Time itself for the first time is HaMakom , The Place, in which we live and move and exist, in which we have not ‘our being’, but the being of the other being at the disposal of another. The temporality of time is The Place which we, embodying, intimately comprehend as the pure ‘at the disposal of another’. Qui vive? The person who begins to fabricate an essentially new world.

Thanks, I was commenting from the perspective that if everyone had a connection with spirit there would be no need for the division. If all was enlightened/One, then of what purpose would be the separation?

Perhaps everything is, "enlightened/One", but the separation is more fun.

Below you can see the horizon pic posted by Androgynus and some blocks have been moved around
to show that the picture has analogous colour that represents true light. Even if the block is only
moved slightly the difference can be seen. The pic is still only a representation of the reality no matter
how detailed it is.

The next picture is a representation of a boat, the horizon, some sea birds and clouds...it gives the perspective
of some form of imagined reality, even though the sea and the sky are the same colour.
The wavy bottom of the boat gives a representaion of motion, but nothing is moving.

The next picture mixes up some of the shapes we would like to recognise, but you could still imagine the
scene...or not, depending on your frame of mind

The last pic in the row has really lost it and without the previous pics you would probably never relate the
pic to a boat, the horizon, some sea birds and clouds .

Below once again is the horizon pic posted by Androgynus, but this time the pic is turned on its head and
the sun is placed in a different perspective. You can see how the mind does not want to cope with this
it looks rubbish, however the last two pics are a painted representation of the horizon and when the same is
done with this pic, although different, the picture can still be categorised as something recognised.

The first pic is analogous to something real and known, the second pic is not and thus we create what we
want it to be. What do you see in that last pic? Was it the same as me?

Here are some shapes being created from two dimention to three dimentional images.

Cube, Tetrahedron, Octahedron, Icosahedron, Dodekahedron

No more real than your triangle Albion, just a series of frames, but percieved as a structure
nonetheless.

We know there is nothing, but look around you and see what we created from it.

Amazing!

And here you see I'm happy just from a yellow filled black circle two black dots and three curvy black lines.

How real are they now? Can you see the beauty in my added pics, which might only be
observed by thier absence

HaMakom a name for God This is similar to how a person may be called by: his first name, 'Dad', 'Captain', 'Honey', 'Sir', etc.
depending on the role being played, and who is talking. What is in a name...would I mind if my son called me by my first name
rather than Dad? Possibly, but he doesn’t.